Author Topic: On The Axioms & Corollaries Of Temporal Transforms  (Read 11963 times)

GrayLensman

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On The Axioms & Corollaries Of Temporal Transforms
« on: January 29, 2004, 07:11:14 pm »
This is a scenario I described to Zeality in a chat session recently.  It pertains to one of the Axioms, namely:

Quote from: warmgun

How Changing the Past Affects Those Time Travelers whose Past Now No Longer Exists

Assume there is a man that by a time, X, has experienced a certain set of events, {E1, E2, E3, E4...E(inf)}. Assume an event, E4, occurs at a time Y. Suppose the man travels to a time T, where T<Y. If time is altered at a time A, where T<A<Y, so as to eliminate E4, the man remains exactly the same as though the time change at A never happened and the causal effects leading the man to time T remain.


If Crono time travels from 1000 AD to 600 AD, the original timeline from 600 AD onward is sent into the Darkness Beyond Time.  A new timeline is instantaneously created, containing all of the changes Crono made to the past.

Crono's past world line is sent into the darkness along with everything else.  This means it is impossible to change anything about Crono's past, prior to him entering the Time Gate in 1000 AD.  No changes made to the new timeline, for all time, can prevent Crono from emerging from a Gate in 600 AD.  Even if the world is destroyed millions of years earlier, Crono would simply emerge from the Gate into empty space.

Now, if Crono returns to 1000 AD through a Gate, he is not changing the (relative) past, so no new timeline is created.  Traveling into the future does not protect Crono from changes to his world line from 600 AD onwards.  If someone else were to travel to a time period prior to 600 AD, Crono's present existence in 1000 AD would be destroyed (sent into the darkness).  Crono would emerge from the Time Gate in 600 AD into a new timeline created by the other traveler.

This means that Crono can rewrite the future world lines of the three Guru's.  They are not afforded any protection from Crono's meddling by their forward time travel.  The original future versions of the gurus are sent into the Darkness Beyond Time.  However, Magus traveled backwards through time.  The Prophet had full protection from any changes he made to his past world line.

GrayLensman

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« Reply #1 on: January 31, 2004, 04:01:16 am »
Relativistic Time Flow Principle

The rate of time in each time period should not be the same.  Relativistic effects produced by changes in the earth and sun's velocity would result in minute time dilations.   Thus, each time period would have its own relative time rate, dependent on relativistic factors.  

This introduces a further complexity to the "Determining the Destination of Time Travel" axiom.  Time Gate apertures and Epoch destinations follow the natural flow of time in their era, but since the time rate of each time period is unique, there would be a discrepancy in the translation of both ends of a Gate into the future.  

For example, if Crono were to warp from  1000 AD to 400 years in the past, the time he spent in 600 AD is not necessarily the same as the time he was away from 1000 AD.  Luckily, Crono could not return to 1000 AD before he left, so there is no worry about causality.

For most time periods this discrepancy should be very small, perhaps on the order of seconds.  However, 65 million BC might experience a significant time dilation.

The Unknowuser_

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« Reply #2 on: February 06, 2004, 12:05:48 am »
I have something to share!

Ok, first, I’m new here  :D (new in posts, I’ve read almost all the topics), second, sorry about my English, I’m from Chile (South America) and here we talk Spanish.

Now, lets focus on this:

Quote
Determining the Destination of Time Travel via Epoch and Time Gates
warmgun wrote:
Time Gates and Epoch have the unique ability of knowing a person's personal time. These things know how long a person has spent in certain times. These devices work under the following principle:

At time X, a person enters Epoch and chooses a certain time, Y, on Epoch's dial, where |X-Y| = Z. In time Y, the person stays for a certain duration, T. When he chooses time X from Epoch's dial, it does not take him to time X. It takes him to time X+T. So the total amount of time this person just traveled from time Y is Z. This quantity, Z, is constant. Likewise, when this person enters a time gate, the same rules apply. The only difference is that Z cannot be chosen from a dial, it is inherent to the time gate and is constant.

Granted, this may seem overly technical, but it provides great insight. For example, this rule proves that time MUST flow a the End of Time. While Epoch has it listed as infinity (inf), the time gates and Epoch treat time travel to and from it as inf-Z and inf+Z. In other words, time flows.


Think on the first trip to 600AD: Marle warps to 600AD. Then, a few minutes later, Chrono goes too and later on (some hours, I think) Lucca enters the gate, right? So, we have three DIFFERENT personal times to each character, because Marle spent more time in 600AD than Chrono, and Chrono spent more time than Lucca (Marle > Chrono > Lucca)

When they came back to 1000AD Lucca should arrive first, later on should arrive Chrono and then Marle (because T is different for each one), but we see them arriving at the same time  :!: . So, the time gates only works with the Z variant that, we know, is constant:

 :arrow:  The gate in Leene Square goes 400 years in the past or (the gate on 600AD goes 400 years in the future) so, Z=400.
 :arrow:  At any point in time, if you enter to the gate, it’ll always take you to X-Z or X+Z instead of X±Z+T because T doesn’t have any relevance to the gate.
ie. You are in 1004 AD. You take the gate in Leene Square. That gate won’t take you to 600AD because Z=400, X-Z=Y => 1004-400=604, Y=604 <= you’ll arrive in this year. Now, say you stay there 3 years (why? I don’t know) so now X=607. lets go inside the gate!: X+Z=Y => 607+400=1007, Y=1007 <= you arrive in this year. Note that the gate doesn’t remembers your “personal time” (T), it only applies the Z variant (that is constant) to the actual time period.

It’s a little confusing, yes, I know, but basically is the same principle WITHOUT the T variant. It should read like this:

(Modified from the original principle )
Quote
“At time X, a person enters Epoch and chooses a certain time, Y, on Epoch's dial, where |X-Y| = Z. In time Y, the person stays for a certain duration, T so now Y=Y+T. When he chooses time X from Epoch's dial, it does not take him to time X. It takes him to time Y+Z. So the total amount of time this person just traveled from time Y is Z. This quantity, Z, is constant. Likewise, when this person enters a time gate, the same rules apply. The only difference is that Z cannot be chosen from a dial, it is inherent to the time gate and is constant.”

This explains quite well how time Gates works. As for the Epoch, since Belthasar is the Guru of Reason (he’s a VERY good scientist), and the computers in 2300AD were able to find Time Gates, I think that he managed to link the Epoch to the Gates in order to make it (the Epoch) capable to Time Travel.

ZeaLitY

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On The Axioms & Corollaries Of Temporal Transforms
« Reply #3 on: February 06, 2004, 01:20:20 am »
Ah, the English is excellent. We wouldn't have known you aren't naturally English-speaking if you had not told us. This is an unprecedented debut on the forums! Your revision is extremely important, as the mechanics of time travel are one of the largest topics in the series and display that the games are consistent with one another. Since this is an actual contribution to an Article, and an excellent one, welcome to the ranks of Chrono Scholars!

The Unknowuser_

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« Reply #4 on: February 06, 2004, 01:14:08 pm »
Uff... Thank you, ZeaLitY, I'm so happy that you liked my little revision  :D … and to be ranked as a Chrono Scholar!!!  8) I didn’t think that this would ever happened. I really appreciate this. (Oh, God, I’m speechless… :lol: )

I promise that I’ll do my best from now on. (Well, my ISP is TOO slow and I have limited time to go online so don’t hope to see me around for a while… but you can always find me via E-Mail)

Thanks again and see you soon! :wink:

doulifee

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On The Axioms & Corollaries Of Temporal Transforms
« Reply #5 on: February 09, 2004, 01:42:31 pm »
That means the gate slice throught the time or they are there at any time ? if you can travel at 600, 607 or 610 like unknowuser told us  you can found the gate at 2300 too ?  If you were able to rest in the area 600 for 1300 year ( so in 1900) you will be drop to 2300 ad ! (i just exagerating the amount of time for my theory.

Another theory the 600/1000 time gate look like stable through this era. why does she sent you in the past at 1000 and in the futur in 600 ?

The Unknowuser_

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« Reply #6 on: February 09, 2004, 06:09:10 pm »
:idea: Theory: Each gate can “live” only for X years/months/weeks/days/hours/seconds…I think…

The gate at 600 A.D. and the one at 1000 A.D. aren’t the same. They’re only a manifestation of each other. The one at Leene Square it’s a link to the one that is on Truce Canyon and Vice-versa. One of them is the original (the one who was created first AND created its link in another time period). I don’t know which one is, but when it disappears, the other one disappears as well (because they’re linked!!!)

 :arrow: So, if the 600 A.D. gate is the original and it died (disappeared) in 607 (I’m speculating), this effect also applies to its link, destroying the gate that is 400 years on the future. (607+400=1007)

Maybe the gate disappeared just a few years later, maybe more, maybe less.

---------------------------------------------------------------

Can anybody help with this?

Quote
Gaspar wrote:
When 4 or more beings step into a time warp, the Conservation of Time theorem states that they will turn up at the space-time coordinates of least resistance. Here. [End of Time]


Then, why after you visit the End of Time for the first time every gate leads you there even if in your party there are only 3 “beings”?.

When you arrive to the [EoF] you have to left a party member there, right? After that, when you have to go back to 600 A.D. (from 1000 A.D.) you have only 3 party members but you still end on the [EoT], no matter which gate you use. (Why!!)

By the way, you can call me Unk if you want…  8)

Kamek

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« Reply #7 on: February 10, 2004, 01:41:17 am »
Gaspar states that all eras link to the End of Time, which is supposed to explain how you can change out your party members at any given time, regardless of the party's distance from the nearest Gate or Epoch... but that could also explain why the gates lead back to the End of Time

However there needs to be more of an explanation because the gates didn't start leading the party to the End of Time until after they broke the 3-person rule and wound up at the End of Time.

There's also the issue of the gate at Proto Dome... where, or when, does that Gate REALLY lead? All the other Gates found by the party have some counterpart at another point in time, except for the one at the Proto Dome.

Then, there's the matter of, after Lavos crashed down in 65 million BC, the Gate left behind leads DIRECTLY to 12,000 BC, WITHOUT taking the party to the End of Time like all the other Gates did.

There's gotta be something more to these Gates than we're giving them credit for... If the Entity created these Gates, could it be possible that it gave them some kind of sentinent ability? They keep track of time, they keep track of whether or not someone's been to the End of Time, and they even allowed Lucca to retrieve Doan from the bad future before it disappeared!

The Entity rewarded Lucca for saving the forest with the red Gate, why not reward her for saving the future by allowing her to bring Doan back from the bad future to give his thanks?

doulifee

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« Reply #8 on: February 10, 2004, 10:40:27 am »
Possible that the end of time is there during a gate translation because you "know" he is here or maybe you know how to reach it ? the gate from lavos crash in prehistoric time to zeal era is maybe to "new" to be added to this principle, that why you need to travel at least once in it.

And yes if time portal are linked by pair, everybody as noticed there is 9 door in the end of time.
Hypothesis 1 : the sister door of the proto dome doesn't exist anymore. maybe i use Unk theory it's possible to a gate to survive without her conterpart.

Hypothesis 2 : The sister door lead to a time where the planet was finally devoured completely by lavos or his spawn.

and just about the ability to change character anytime you want, it look like the black bird was timeproof  :)

The Unknowuser_

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« Reply #9 on: February 10, 2004, 12:44:40 pm »
Hypotesis 1 sounds good to me, if you want H2 to work, you still need the gate's counterpart on the end of time (even if the world is destroyed at that point, the gate works).

H3: The sister door of the proto dome is the one at the end of time. (...)

doulifee

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« Reply #10 on: February 10, 2004, 02:41:51 pm »
Quote from: The Unknowuser_
Hypotesis 1 sounds good to me, if you want H2 to work, you still need the gate's counterpart on the end of time (even if the world is destroyed at that point, the gate works).

H3: The sister door of the proto dome is the one at the end of time. (...)

About H2 i want to say when the planet was completly destroy i.e does not exist anymore


that doesn't make sense for H3 because that means all gate had their counter part in the EOT ? so why you don't pass by there ? Or maybe we can add a law of an open door to the Eot only if you break the 3 members rules? so why the guru is there (he came alone)?

I forgot the guru came their by a lavos' portal not a entity's one....

The Unknowuser_

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« Reply #11 on: February 11, 2004, 12:02:03 am »
Quote from: doulifee
About H2 i want to say when the planet was completly destroy i.e does not exist anymore


Ups...  :oops:

ZeaLitY

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« Reply #12 on: February 12, 2004, 07:00:09 pm »
GrayLensman, Ybrik and I came up with something. First, it should be known that Gaspar specifically built the platform to hold the nine Gates.

Gaspar-Control Theory
GrayLensman


All time Gates naturally connect two points in time and space, but at times each travel destination may connect to the End of Time.  Other than Spekkio, Gaspar is the only person who resides there. Since Gaspar is the Guru of Time, I speculate that he is solely responsible for Gates connecting to the End of Time, Conservation of Time theorem nonwithstanding. He arbitrarily decides if and when Gates will connect to the pillars at the End of Time.
---

Lingering problems and such:

Lavos 'gates' have a tendency to disperse people in proximity to different eras. In the Ocean Palace, the gurus and Janus were spread apart. Yet, in Magus's Lair, the 'gate' produced by Lavos sends Crono's party to 65,000,000 B.C. and Magus to 12,000 B.C., rather than spreading them across time.

Singular-Wormhole Theory
ZeaLitY


In the Ocean Palace, each guru went through a different gate. It can thus be proposed that Crono's entire party went through one wormhole, and Magus through another, as he was standing on the opposite side of the summoning room at the time of the distortion.
---

Kamek noted that the Gate exposed by Lavos's crashing into the planet takes one directly to 12,000 B.C. without stopping at the End of Time. Ybrik Metaknight noted that, "if you go back through the gate in 12,000 immediately after going through it the first time, you end up at the End of Time." He also observed that "once more after Magus and Schala send you back, you immediately emerge in 65,000,000 B.C." These can be accounted for by the Gaspar-Control Theory. Ybrik Metaknight also speculates that they are story devices; that having the party stop along the way after the 65,000,000 BC Gate is exposed would disrupt the game's flow.

Kamek

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« Reply #13 on: February 13, 2004, 12:01:53 am »
The only problem I see is the Gate that sucked away Janus and Melchior after the Ocean Palace Disaster, Version 2, where Version 1 is how Magus remembers it, and Version 2 is how the time travelers experienced it.

Quote
ELDER: When the disaster struck, an
   eerie, black portal materialized.
   Melchior tried to save Janus, but he
   was also dragged in.

From this I'm inferring that both Janus and Melchior fell into the same Gate. There is no mention of when the two were sent, but it is inferred that if the timeline is to be preserved, Janus must have been sent to 600-ish AD and Melchior to 1000-ish AD.

Speaking of Version 1 of the Ocean Palace Disaster... It is my belief that the following Gates were created when the Disaster struck, by viewing the cutscenes where Janus and the three Gurus materialized in their new time period...

1000 AD (Medina Village)
2300 (Bangor? Proto? Dome)
??? (End of Time)
600 AD (Truce Canyon)

My guess is that the gate at Truce Canyon (Leene Square in 1000 AD) was somehow re-activated by the Telepod accident. Marle's pendant may possibly have had a small amount of Lavos's power left in it, which somehow combined with the Telepod's energy and "ripped" open the Gate. There may have been some kind of gravitational or other type of force which caused Marle to drop the pendant. When the accident was repeated with Crono holding the pendant instead, he no doubt held on very tightly as Lucca advised him to.

However this doesn't explain how the gate at 1000 AD Medina Village got linked to 65 million BC Mystic Mountain, or how the gate at 2300 AD got linked to wherever it ended up linking to.

Nor does this explain how Lucca was able to make a Gate Key using only the Telepod's technology, but it's a start for now.

doulifee

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« Reply #14 on: February 13, 2004, 12:17:52 pm »
it look like Lavos' gate  have a short life and are very unstable. If magus was dropped at the dark ages (external part of the gate) and the party at prehistoric time (center of the gate) you can apply the same to the small gate were janus and melch were both dragged

and about the telepod and the portal could it be possible that the mechanism emit waves similar to the mammon machine, not powerful enough to reactivate the pendant but enough to open a gate. that maybe how lucca has created the gate key. (she can open "time" door not "zealian" door)